Abstract
A new Monte Carlo based method is presented for estimating the system reliability of constraint bounded design spaces. The new method is first developed in its general form, which is applicable to any joint probability distribution. It is also demonstrated that this method can be used to concurrently estimate derivatives of the system reliability (e.g., for use in gradient-based numerical optimization). The method is then specialized to the particular case of an n-dimensional Gaussian (normal) distribution, which allows for a simpler form. An important property of probability distributions, the dead band effect, is also presented, and it is shown that this effect has important ramifications for the application of the shooting Monte Carlo approach. Finally, numerical values are presented that demonstrate improved efficiencies of up to orders of magnitude relative to the conventional Monte Carlo approach.
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